We can observe from Table REF  that in such a scenario PELT, SMUCE, CL, WBS sSIC, FDR and robseg (Huber) are all not robust with respect to the outliers and they all overestimate the number of changepoints due to fitting the outliers. The CBS and cumSeg still systematically underestimate the number of changepoints. It is not that surprising robseg (biweight) proposed in [1]} is quite robust in this scenario since it was designed to handle such an issue. It shows a very high frequency 0.956 to recover the correct number of changepoints. Moreover, from the quantity of empirical risk \(\widehat{R}_{n}(\cdot )\) , it turns out robseg (biweight) outperforms all the other candidates significantly which also indicates an excellent performance of localising the changepoints as well as estimating the value of \({\gamma }^{*}\)  on each segment. Our selection procedure automatically gives the preference to robseg (biweight) in this case with frequency 1.000 which confirms the stability of our selection rule practically.
